9 papers
Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two
Stevan Gajović, Sun Woo Park
We prove that for any number field and any fixed genus , there are infinitely many non-isomorphic hyperelliptic curves of genus over whose Jacobians have rank…
Pythagoras numbers for infinite algebraic fields
Nicolas Daans, Stevan Gajović, Siu Hang Man +1
We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic…
The density of elliptic curves over with a rational 3-torsion point or a rational 3-isogeny
Stevan Gajović, Lazar Radičević, Matteo Verzobio
We determine the probability that a random Weierstrass equation with coefficients in the -adic integers defines an elliptic curve with a non-trivial -torsion point, or with a…
Arithmetic-geometric mean sequences over finite fields , where
Natália Bátorová, Stevan Gajović
Arithmetic-geometric mean sequences were already studied over real and complex numbers, and recently, Michael J. Griffin, Ken Ono, Neelam Saikia and Wei-Lun Tsai considered them ov…
Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
Stevan Gajović, Jeroen Hanselman, Angelos Koutsianas
In this paper, we prove that the local-global principle of -isogenies for elliptic curves over quadratic fields does not fail. This gives a positive answer to a conjecture by B…
On -adic denseness of quotients of values of integral forms
Deepa Antony, Rupam Barman, Stevan Gajović +1
Given , the ratio set or the quotient set of is defined by . It is an open problem to study the denseness of in the …